src/gromacs/linearalgebra/gmx_lapack.h

   1 /*
   2  * This file is part of the GROMACS molecular simulation package.
   3  *
   4  * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
   5  * Copyright (c) 2001-2008, The GROMACS development team.
   6  * Copyright (c) 2012,2013,2014,2019, by the GROMACS development team, led by
   7  * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
   8  * and including many others, as listed in the AUTHORS file in the
   9  * top-level source directory and at http://www.gromacs.org.
  10  *
  11  * GROMACS is free software; you can redistribute it and/or
  12  * modify it under the terms of the GNU Lesser General Public License
  13  * as published by the Free Software Foundation; either version 2.1
  14  * of the License, or (at your option) any later version.
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  19  * Lesser General Public License for more details.
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  36  */
  37 /*! \internal \file
  38  * \brief
  39  * Header definitions for the standard LAPACK library.
  40  *
  41  * This is the subset of LAPACK routines used for the
  42  * linear algebra operations in Gromacs. Most of the execution time
  43  * will be spent in the BLAS routines, which you hopefully have an
  44  * optimized version of. Gromacs includes reference implementations
  45  * of both BLAS and LAPACK so it compiles everywhere, but you should
  46  * really try to find a vendor or otherwise optimized version at least
  47  * of BLAS for better performance.
  48  *
  49  * Do NOT use this code for other purposes - we only provide this as a
  50  * simple fallback/reference implementation when no optimized BLAS
  51  * is present. If you need an implementation for your own code
  52  * there are several much faster versions out there.
  53  *
  54  * All routines are compatible with the LAPACK/BLAS reference implementations,
  55  * meaning they assume fortran-style matrix row/column organization.
  56  *
  57  * There is plenty of documentation for these routines available
  58  * at http://www.netlib.org/lapack , so there is no point in repeating
  59  * it here.
  60  */
  61 #ifndef GMX_LAPACK_H
  62 #define GMX_LAPACK_H
  63
  64 /*! \cond */
  65
  66 #include "config.h"
  67
  68 /* These are not required by this file, but by the internal LAPACK
  69  * implementation.  In principle, they could be included in each file
  70  * that requires them, but this is simpler.  Since the header is internal
  71  * to the linearyalgebra/ module, the added complexity may not be worth it. */
  72 #include "gromacs/utility/basedefinitions.h"
  73 #include "gromacs/utility/real.h"
  74
  75 #ifdef __cplusplus
  76 extern "C"
  77 {
  78 #endif
  79 #if 0
  80 }
  81 #endif
  82     /* Double precision */
  83
  84     void F77_FUNC(dbdsdc, DBDSDC)(const char* uplo,
  85                                   const char* compq,
  86                                   int*        n,
  87                                   double*     d,
  88                                   double*     e,
  89                                   double*     u,
  90                                   int*        ldu,
  91                                   double*     vt,
  92                                   int*        ldvt,
  93                                   double*     q,
  94                                   int*        iq,
  95                                   double*     work,
  96                                   int*        iwork,
  97                                   int*        info);
  98
  99     void F77_FUNC(dgetf2, DGETF2)(int* m, int* n, double* a, int* lda, int* ipiv, int* info);
 100
 101     void F77_FUNC(dlamrg, DLAMRG)(int* n1, int* n2, double* a, int* dtrd1, int* dtrd2, int* index);
 102
 103     void F77_FUNC(dlarnv, DLARNV)(int* idist, int* iseed, int* n, double* x);
 104
 105     void F77_FUNC(dlasd0, DLASD0)(int*    n,
 106                                   int*    sqre,
 107                                   double* d,
 108                                   double* e,
 109                                   double* u,
 110                                   int*    ldu,
 111                                   double* vt,
 112                                   int*    ldvt,
 113                                   int*    smlsiz,
 114                                   int*    iwork,
 115                                   double* work,
 116                                   int*    info);
 117
 118     void F77_FUNC(dlasda, DLASDA)(int*    icompq,
 119                                   int*    smlsiz,
 120                                   int*    n,
 121                                   int*    sqre,
 122                                   double* d,
 123                                   double* e,
 124                                   double* u,
 125                                   int*    ldu,
 126                                   double* vt,
 127                                   int*    k,
 128                                   double* difl,
 129                                   double* difr,
 130                                   double* z,
 131                                   double* poles,
 132                                   int*    givptr,
 133                                   int*    givcol,
 134                                   int*    ldgcol,
 135                                   int*    perm,
 136                                   double* givnum,
 137                                   double* c,
 138                                   double* s,
 139                                   double* work,
 140                                   int*    iwork,
 141                                   int*    info);
 142
 143     void F77_FUNC(dlasq6, DLASQ6)(int*    i0,
 144                                   int*    n0,
 145                                   double* z,
 146                                   int*    pp,
 147                                   double* dmin,
 148                                   double* dmin1,
 149                                   double* dmin2,
 150                                   double* dn,
 151                                   double* dnm1,
 152                                   double* dnm2);
 153
 154     void F77_FUNC(dorgl2,
 155                   DORGL2)(int* m, int* n, int* k, double* a, int* lda, double* tau, double* work, int* info);
 156
 157     void F77_FUNC(dbdsqr, DBDSQR)(const char* uplo,
 158                                   int*        n,
 159                                   int*        ncvt,
 160                                   int*        nru,
 161                                   int*        ncc,
 162                                   double*     d,
 163                                   double*     e,
 164                                   double*     vt,
 165                                   int*        ldvt,
 166                                   double*     u,
 167                                   int*        ldu,
 168                                   double*     c,
 169                                   int*        ldc,
 170                                   double*     work,
 171                                   int*        info);
 172
 173     void F77_FUNC(dgetrf, DGETRF)(int* m, int* n, double* a, int* lda, int* ipiv, int* info);
 174
 175     void F77_FUNC(dgetri,
 176                   DGETRI)(int* n, double* a, int* lda, int* ipiv, double* work, int* lwork, int* info);
 177
 178     void F77_FUNC(dgetrs, DGETRS)(const char* trans,
 179                                   int*        n,
 180                                   int*        nrhs,
 181                                   double*     a,
 182                                   int*        lda,
 183                                   int*        ipiv,
 184                                   double*     b,
 185                                   int*        ldb,
 186                                   int*        info);
 187
 188     void F77_FUNC(dtrtri,
 189                   DTRTRI)(const char* uplo, const char* diag, int* n, double* a, int* lda, int* info);
 190
 191     void F77_FUNC(dtrti2,
 192                   DTRTI2)(const char* uplo, const char* diag, int* n, double* a, int* lda, int* info);
 193
 194     double F77_FUNC(dlange, DLANGE)(const char* norm, int* m, int* n, double* a, int* lda, double* work);
 195
 196     void F77_FUNC(dlarrbx, DLARRBX)(int*    n,
 197                                     double* d,
 198                                     double* l,
 199                                     double* ld,
 200                                     double* lld,
 201                                     int*    ifirst,
 202                                     int*    ilast,
 203                                     double* rtol1,
 204                                     double* rtol2,
 205                                     int*    offset,
 206                                     double* w,
 207                                     double* wgap,
 208                                     double* werr,
 209                                     double* work,
 210                                     int*    iwork,
 211                                     int*    info);
 212
 213     void F77_FUNC(dlasd1, DLASD1)(int*    nl,
 214                                   int*    nr,
 215                                   int*    sqre,
 216                                   double* d,
 217                                   double* alpha,
 218                                   double* beta,
 219                                   double* u,
 220                                   int*    ldu,
 221                                   double* vt,
 222                                   int*    ldvt,
 223                                   int*    idxq,
 224                                   int*    iwork,
 225                                   double* work,
 226                                   int*    info);
 227
 228     void F77_FUNC(dlasdq, DLASDQ)(const char* uplo,
 229                                   int*        sqre,
 230                                   int*        n,
 231                                   int*        ncvt,
 232                                   int*        nru,
 233                                   int*        ncc,
 234                                   double*     d,
 235                                   double*     e,
 236                                   double*     vt,
 237                                   int*        ldvt,
 238                                   double*     u,
 239                                   int*        ldu,
 240                                   double*     c,
 241                                   int*        ldc,
 242                                   double*     work,
 243                                   int*        info);
 244
 245     void F77_FUNC(dlasr, DLASR)(const char* side,
 246                                 const char* pivot,
 247                                 const char* direct,
 248                                 int*        m,
 249                                 int*        n,
 250                                 double*     c,
 251                                 double*     s,
 252                                 double*     a,
 253                                 int*        lda);
 254
 255     void F77_FUNC(dorglq,
 256                   DORGLQ)(int* m, int* n, int* k, double* a, int* lda, double* tau, double* work, int* lwork, int* info);
 257
 258     void F77_FUNC(dormtr, DORMTR)(const char* side,
 259                                   const char* uplo,
 260                                   const char* trans,
 261                                   int*        m,
 262                                   int*        n,
 263                                   double*     a,
 264                                   int*        lda,
 265                                   double*     tau,
 266                                   double*     c,
 267                                   int*        ldc,
 268                                   double*     work,
 269                                   int*        lwork,
 270                                   int*        info);
 271
 272     void F77_FUNC(dgebd2, DGEBD2)(int*    m,
 273                                   int*    n,
 274                                   double* a,
 275                                   int*    lda,
 276                                   double* d,
 277                                   double* e,
 278                                   double* tauq,
 279                                   double* taup,
 280                                   double* work,
 281                                   int*    info);
 282
 283     void F77_FUNC(dlabrd, DLABRD)(int*    m,
 284                                   int*    n,
 285                                   int*    nb,
 286                                   double* a,
 287                                   int*    lda,
 288                                   double* d,
 289                                   double* e,
 290                                   double* tauq,
 291                                   double* taup,
 292                                   double* x,
 293                                   int*    ldx,
 294                                   double* y,
 295                                   int*    ldy);
 296
 297     double F77_FUNC(dlanst, DLANST)(const char* norm, int* n, double* d, double* e);
 298
 299     double F77_FUNC(dlansy,
 300                     DLANSY)(const char* norm, const char* uplo, int* n, double* a, int* lda, double* work);
 301
 302     void F77_FUNC(dlarrex, DLARREX)(const char* range,
 303                                     int*        n,
 304                                     double*     vl,
 305                                     double*     vu,
 306                                     int*        il,
 307                                     int*        iu,
 308                                     double*     d,
 309                                     double*     e,
 310                                     double*     tol,
 311                                     int*        nsplit,
 312                                     int*        isplit,
 313                                     int*        m,
 314                                     double*     w,
 315                                     int*        iblock,
 316                                     int*        indexw,
 317                                     double*     gersch,
 318                                     double*     work,
 319                                     int*        iwork,
 320                                     int*        info);
 321
 322     void F77_FUNC(dlasd2, DLASD2)(int*    nl,
 323                                   int*    nr,
 324                                   int*    sqre,
 325                                   int*    k,
 326                                   double* d,
 327                                   double* z,
 328                                   double* alpha,
 329                                   double* beta,
 330                                   double* u,
 331                                   int*    ldu,
 332                                   double* vt,
 333                                   int*    ldvt,
 334                                   double* dsigma,
 335                                   double* u2,
 336                                   int*    ldu2,
 337                                   double* vt2,
 338                                   int*    ldvt2,
 339                                   int*    idxp,
 340                                   int*    idx,
 341                                   int*    idxc,
 342                                   int*    idxq,
 343                                   int*    coltyp,
 344                                   int*    info);
 345
 346     void F77_FUNC(dlasdt, DLASDT)(int* n, int* lvl, int* nd, int* inode, int* ndiml, int* ndimr, int* msub);
 347
 348     void F77_FUNC(dlasrt, DLASRT)(const char* id, int* n, double* d, int* info);
 349
 350     void F77_FUNC(dlasrt2, DLASRT2)(const char* id, int* n, double* d, int* key, int* info);
 351
 352     void F77_FUNC(ilasrt2, ILASRT2)(const char* id, int* n, int* d, int* key, int* info);
 353
 354     void F77_FUNC(dorgqr,
 355                   DORGQR)(int* m, int* n, int* k, double* a, int* lda, double* tau, double* work, int* lwork, int* info);
 356
 357     void F77_FUNC(dstebz, DSTEBZ)(const char* range,
 358                                   const char* order,
 359                                   int*        n,
 360                                   double*     vl,
 361                                   double*     vu,
 362                                   int*        il,
 363                                   int*        iu,
 364                                   double*     abstol,
 365                                   double*     d,
 366                                   double*     e,
 367                                   int*        m,
 368                                   int*        nsplit,
 369                                   double*     w,
 370                                   int*        iblock,
 371                                   int*        isplit,
 372                                   double*     work,
 373                                   int*        iwork,
 374                                   int*        info);
 375
 376     void F77_FUNC(dsteqr, DSTEQR)(const char* compz,
 377                                   int*        n,
 378                                   double*     d__,
 379                                   double*     e,
 380                                   double*     z__,
 381                                   int*        ldz,
 382                                   double*     work,
 383                                   int*        info);
 384
 385     void F77_FUNC(dgebrd, DGEBRD)(int*    m,
 386                                   int*    n,
 387                                   double* a,
 388                                   int*    lda,
 389                                   double* d,
 390                                   double* e,
 391                                   double* tauq,
 392                                   double* taup,
 393                                   double* work,
 394                                   int*    lwork,
 395                                   int*    info);
 396
 397     void F77_FUNC(dlacpy,
 398                   DLACPY)(const char* uplo, int* m, int* n, double* a, int* lda, double* b, int* ldb);
 399
 400     double F77_FUNC(dlapy2, DLAPY2)(double* x, double* y);
 401
 402
 403     void F77_FUNC(dlarrfx, DLARRFX)(int*    n,
 404                                     double* d,
 405                                     double* l,
 406                                     double* ld,
 407                                     double* lld,
 408                                     int*    ifirst,
 409                                     int*    ilast,
 410                                     double* w,
 411                                     double* sigma,
 412                                     double* dplus,
 413                                     double* lplus,
 414                                     double* work,
 415                                     int*    info);
 416
 417     void F77_FUNC(dlasd3, DLASD3)(int*    nl,
 418                                   int*    nr,
 419                                   int*    sqre,
 420                                   int*    k,
 421                                   double* d,
 422                                   double* q,
 423                                   int*    ldq,
 424                                   double* dsigma,
 425                                   double* u,
 426                                   int*    ldu,
 427                                   double* u2,
 428                                   int*    ldu2,
 429                                   double* vt,
 430                                   int*    ldvt,
 431                                   double* vt2,
 432                                   int*    ldvt2,
 433                                   int*    idxc,
 434                                   int*    ctot,
 435                                   double* z,
 436                                   int*    info);
 437
 438     void F77_FUNC(dlaset,
 439                   DLASET)(const char* uplo, int* m, int* n, double* alpha, double* beta, double* a, int* lda);
 440
 441     void F77_FUNC(dlassq, DLASSQ)(int* n, double* x, int* incx, double* scale, double* sumsq);
 442
 443     void F77_FUNC(dorm2l, DORM2L)(const char* side,
 444                                   const char* trans,
 445                                   int*        m,
 446                                   int*        n,
 447                                   int*        k,
 448                                   double*     a,
 449                                   int*        lda,
 450                                   double*     tau,
 451                                   double*     c,
 452                                   int*        ldc,
 453                                   double*     work,
 454                                   int*        info);
 455
 456     void F77_FUNC(dstegr, DSTEGR)(const char* jobz,
 457                                   const char* range,
 458                                   int*        n,
 459                                   double*     d,
 460                                   double*     e,
 461                                   double*     vl,
 462                                   double*     vu,
 463                                   int*        il,
 464                                   int*        iu,
 465                                   double*     abstol,
 466                                   int*        m,
 467                                   double*     w,
 468                                   double*     z,
 469                                   int*        ldz,
 470                                   int*        isuppz,
 471                                   double*     work,
 472                                   int*        lwork,
 473                                   int*        iwork,
 474                                   int*        liwork,
 475                                   int*        info);
 476
 477     void F77_FUNC(ssteqr,
 478                   SSTEQR)(const char* compz, int* n, float* d__, float* e, float* z__, int* ldz, float* work, int* info);
 479
 480     void F77_FUNC(dgelq2, DGELQ2)(int* m, int* n, double* a, int* lda, double* tau, double* work, int* info);
 481
 482     void F77_FUNC(dlae2, DLAE2)(double* a, double* b, double* c, double* rt1, double* rt2);
 483
 484     void F77_FUNC(dlaev2,
 485                   DLAEV2)(double* a, double* b, double* c, double* rt1, double* rt2, double* cs1, double* cs2);
 486
 487     void F77_FUNC(dlar1vx, DLAR1VX)(int*    n,
 488                                     int*    b1,
 489                                     int*    bn,
 490                                     double* sigma,
 491                                     double* d,
 492                                     double* l,
 493                                     double* ld,
 494                                     double* lld,
 495                                     double* eval,
 496                                     double* gersch,
 497                                     double* z,
 498                                     double* ztz,
 499                                     double* mingma,
 500                                     int*    r,
 501                                     int*    isuppz,
 502                                     double* work);
 503
 504     void F77_FUNC(dlarrvx, DLARRVX)(int*    n,
 505                                     double* d,
 506                                     double* l,
 507                                     int*    isplit,
 508                                     int*    m,
 509                                     double* w,
 510                                     int*    iblock,
 511                                     int*    indexw,
 512                                     double* gersch,
 513                                     double* tol,
 514                                     double* z,
 515                                     int*    ldz,
 516                                     int*    isuppz,
 517                                     double* work,
 518                                     int*    iwork,
 519                                     int*    info);
 520
 521     void F77_FUNC(dlasd4, DLASD4)(int*    n,
 522                                   int*    i,
 523                                   double* d,
 524                                   double* z,
 525                                   double* delta,
 526                                   double* rho,
 527                                   double* sigma,
 528                                   double* work,
 529                                   int*    info);
 530
 531     void F77_FUNC(dlasq1, DLASQ1)(int* n, double* d, double* e, double* work, int* info);
 532
 533
 534     void F77_FUNC(dlasv2, DLASV2)(double* f,
 535                                   double* g,
 536                                   double* h,
 537                                   double* ssmin,
 538                                   double* ssmax,
 539                                   double* snr,
 540                                   double* csr,
 541                                   double* snl,
 542                                   double* csl);
 543
 544     void F77_FUNC(dorm2r, DORM2R)(const char* side,
 545                                   const char* trans,
 546                                   int*        m,
 547                                   int*        n,
 548                                   int*        k,
 549                                   double*     a,
 550                                   int*        lda,
 551                                   double*     tau,
 552                                   double*     c,
 553                                   int*        ldc,
 554                                   double*     work,
 555                                   int*        info);
 556
 557     void F77_FUNC(dstein, DSTEIN)(int*    n,
 558                                   double* d,
 559                                   double* e,
 560                                   int*    m,
 561                                   double* w,
 562                                   int*    iblock,
 563                                   int*    isplit,
 564                                   double* z,
 565                                   int*    ldz,
 566                                   double* work,
 567                                   int*    iwork,
 568                                   int*    ifail,
 569                                   int*    info);
 570
 571     void F77_FUNC(dgelqf,
 572                   DGELQF)(int* m, int* n, double* a, int* lda, double* tau, double* work, int* lwork, int* info);
 573
 574     void F77_FUNC(dlaebz, DLAEBZ)(int*    ijob,
 575                                   int*    nitmax,
 576                                   int*    n,
 577                                   int*    mmax,
 578                                   int*    minp,
 579                                   int*    nbmin,
 580                                   double* abstol,
 581                                   double* reltol,
 582                                   double* pivmin,
 583                                   double* d,
 584                                   double* e,
 585                                   double* e2,
 586                                   int*    nval,
 587                                   double* ab,
 588                                   double* c,
 589                                   int*    mout,
 590                                   int*    nab,
 591                                   double* work,
 592                                   int*    iwork,
 593                                   int*    info);
 594
 595     void F77_FUNC(dlarf, DLARF)(const char* side,
 596                                 int*        m,
 597                                 int*        n,
 598                                 double*     v,
 599                                 int*        incv,
 600                                 double*     tau,
 601                                 double*     c,
 602                                 int*        ldc,
 603                                 double*     work);
 604
 605     void F77_FUNC(dlartg, DLARTG)(double* f, double* g, double* cs, double* sn, double* r);
 606
 607     void F77_FUNC(dlasd5,
 608                   DLASD5)(int* i, double* d, double* z, double* delta, double* rho, double* dsigma, double* work);
 609
 610     void F77_FUNC(dlasq2, DLASQ2)(int* n, double* z, int* info);
 611
 612     void F77_FUNC(dlasq3, DLASQ3)(int*    i0,
 613                                   int*    n0,
 614                                   double* z,
 615                                   int*    pp,
 616                                   double* dmin,
 617                                   double* sigma,
 618                                   double* desig,
 619                                   double* qmax,
 620                                   int*    nfail,
 621                                   int*    iter,
 622                                   int*    ndiv,
 623                                   int*    ieee);
 624
 625     void F77_FUNC(dlaswp, DLASWP)(int* n, double* a, int* lda, int* k1, int* k2, int* ipiv, int* incx);
 626
 627     void F77_FUNC(dormbr, DORMBR)(const char* vect,
 628                                   const char* side,
 629                                   const char* trans,
 630                                   int*        m,
 631                                   int*        n,
 632                                   int*        k,
 633                                   double*     a,
 634                                   int*        lda,
 635                                   double*     tau,
 636                                   double*     c,
 637                                   int*        ldc,
 638                                   double*     work,
 639                                   int*        lwork,
 640                                   int*        info);
 641
 642     void F77_FUNC(dsterf, DSTERF)(int* n, double* d, double* e, int* info);
 643
 644     void F77_FUNC(dgeqr2, DGEQR2)(int* m, int* n, double* a, int* lda, double* tau, double* work, int* info);
 645
 646     void F77_FUNC(dlaed6, DLAED6)(int*    kniter,
 647                                   int*    orgati,
 648                                   double* rho,
 649                                   double* d,
 650                                   double* z,
 651                                   double* finit,
 652                                   double* tau,
 653                                   int*    info);
 654
 655     void F77_FUNC(dlarfb, DLARFB)(const char* side,
 656                                   const char* trans,
 657                                   const char* direct,
 658                                   const char* storev,
 659                                   int*        m,
 660                                   int*        n,
 661                                   int*        k,
 662                                   double*     v,
 663                                   int*        ldv,
 664                                   double*     t,
 665                                   int*        ldt,
 666                                   double*     c,
 667                                   int*        ldc,
 668                                   double*     work,
 669                                   int*        ldwork);
 670
 671     void F77_FUNC(dlaruv, DLARUV)(int* iseed, int* n, double* x);
 672
 673     void F77_FUNC(dlasd6, DLASD6)(int*    icompq,
 674                                   int*    nl,
 675                                   int*    nr,
 676                                   int*    sqre,
 677                                   double* d,
 678                                   double* vf,
 679                                   double* vl,
 680                                   double* alpha,
 681                                   double* beta,
 682                                   int*    idxq,
 683                                   int*    perm,
 684                                   int*    givptr,
 685                                   int*    givcol,
 686                                   int*    ldgcol,
 687                                   double* givnum,
 688                                   int*    ldgnum,
 689                                   double* poles,
 690                                   double* difl,
 691                                   double* difr,
 692                                   double* z,
 693                                   int*    k,
 694                                   double* c,
 695                                   double* s,
 696                                   double* work,
 697                                   int*    iwork,
 698                                   int*    info);
 699
 700     void F77_FUNC(dlatrd, DLATRD)(const char* uplo,
 701                                   int*        n,
 702                                   int*        nb,
 703                                   double*     a,
 704                                   int*        lda,
 705                                   double*     e,
 706                                   double*     tau,
 707                                   double*     w,
 708                                   int*        ldw);
 709
 710     void F77_FUNC(dorml2, DORML2)(const char* side,
 711                                   const char* trans,
 712                                   int*        m,
 713                                   int*        n,
 714                                   int*        k,
 715                                   double*     a,
 716                                   int*        lda,
 717                                   double*     tau,
 718                                   double*     c,
 719                                   int*        ldc,
 720                                   double*     work,
 721                                   int*        info);
 722
 723     void F77_FUNC(dstevr, DSTEVR)(const char* jobz,
 724                                   const char* range,
 725                                   int*        n,
 726                                   double*     d,
 727                                   double*     e,
 728                                   double*     vl,
 729                                   double*     vu,
 730                                   int*        il,
 731                                   int*        iu,
 732                                   double*     abstol,
 733                                   int*        m,
 734                                   double*     w,
 735                                   double*     z,
 736                                   int*        ldz,
 737                                   int*        isuppz,
 738                                   double*     work,
 739                                   int*        lwork,
 740                                   int*        iwork,
 741                                   int*        liwork,
 742                                   int*        info);
 743
 744     void F77_FUNC(dsytrd, DSYTRD)(const char* uplo,
 745                                   int*        n,
 746                                   double*     a,
 747                                   int*        lda,
 748                                   double*     d,
 749                                   double*     e,
 750                                   double*     tau,
 751                                   double*     work,
 752                                   int*        lwork,
 753                                   int*        info);
 754
 755     void F77_FUNC(dsyevr, DSYEVR)(const char* jobz,
 756                                   const char* range,
 757                                   const char* uplo,
 758                                   int*        n,
 759                                   double*     a,
 760                                   int*        lda,
 761                                   double*     vl,
 762                                   double*     vu,
 763                                   int*        il,
 764                                   int*        iu,
 765                                   double*     abstol,
 766                                   int*        m,
 767                                   double*     w,
 768                                   double*     z__,
 769                                   int*        ldz,
 770                                   int*        isuppz,
 771                                   double*     work,
 772                                   int*        lwork,
 773                                   int*        iwork,
 774                                   int*        liwork,
 775                                   int*        info);
 776
 777     void F77_FUNC(dormql, DORMQL)(const char* side,
 778                                   const char* trans,
 779                                   int*        m,
 780                                   int*        n,
 781                                   int*        k,
 782                                   double*     a,
 783                                   int*        lda,
 784                                   double*     tau,
 785                                   double*     c,
 786                                   int*        ldc,
 787                                   double*     work,
 788                                   int*        lwork,
 789                                   int*        info);
 790
 791     void F77_FUNC(dormqr, DORMQR)(const char* side,
 792                                   const char* trans,
 793                                   int*        m,
 794                                   int*        n,
 795                                   int*        k,
 796                                   double*     a,
 797                                   int*        lda,
 798                                   double*     tau,
 799                                   double*     c,
 800                                   int*        ldc,
 801                                   double*     work,
 802                                   int*        lwork,
 803                                   int*        info);
 804
 805     void F77_FUNC(dorgbr, DORGBR)(const char* vect,
 806                                   int*        m,
 807                                   int*        n,
 808                                   int*        k,
 809                                   double*     a,
 810                                   int*        lda,
 811                                   double*     tau,
 812                                   double*     work,
 813                                   int*        lwork,
 814                                   int*        info);
 815
 816     void F77_FUNC(dlasq5, DLASQ5)(int*    i0,
 817                                   int*    n0,
 818                                   double* z,
 819                                   int*    pp,
 820                                   double* tau,
 821                                   double* dmin,
 822                                   double* dmin1,
 823                                   double* dmin2,
 824                                   double* dn,
 825                                   double* dnm1,
 826                                   double* dnm2,
 827                                   int*    ieee);
 828
 829     void F77_FUNC(dlasd8, DLASD8)(int*    icompq,
 830                                   int*    k,
 831                                   double* d,
 832                                   double* z,
 833                                   double* vf,
 834                                   double* vl,
 835                                   double* difl,
 836                                   double* difr,
 837                                   int*    lddifr,
 838                                   double* dsigma,
 839                                   double* work,
 840                                   int*    info);
 841
 842     void F77_FUNC(dlascl, DLASCL)(const char* type,
 843                                   int*        kl,
 844                                   int*        ku,
 845                                   double*     cfrom,
 846                                   double*     cto,
 847                                   int*        m,
 848                                   int*        n,
 849                                   double*     a,
 850                                   int*        lda,
 851                                   int*        info);
 852
 853     void F77_FUNC(dlarft, DLARFT)(const char* direct,
 854                                   const char* storev,
 855                                   int*        n,
 856                                   int*        k,
 857                                   double*     v,
 858                                   int*        ldv,
 859                                   double*     tau,
 860                                   double*     t,
 861                                   int*        ldt);
 862
 863     void F77_FUNC(dlagts, DLAGTS)(int*    job,
 864                                   int*    n,
 865                                   double* a,
 866                                   double* b,
 867                                   double* c,
 868                                   double* d,
 869                                   int*    in,
 870                                   double* y,
 871                                   double* tol,
 872                                   int*    info);
 873
 874     void F77_FUNC(dgesdd, DGESDD)(const char* jobz,
 875                                   int*        m,
 876                                   int*        n,
 877                                   double*     a,
 878                                   int*        lda,
 879                                   double*     s,
 880                                   double*     u,
 881                                   int*        ldu,
 882                                   double*     vt,
 883                                   int*        ldvt,
 884                                   double*     work,
 885                                   int*        lwork,
 886                                   int*        iwork,
 887                                   int*        info);
 888
 889     void F77_FUNC(dsytd2,
 890                   DSYTD2)(const char* uplo, int* n, double* a, int* lda, double* d, double* e, double* tau, int* info);
 891
 892     void F77_FUNC(dormlq, DORMLQ)(const char* side,
 893                                   const char* trans,
 894                                   int*        m,
 895                                   int*        n,
 896                                   int*        k,
 897                                   double*     a,
 898                                   int*        lda,
 899                                   double*     tau,
 900                                   double*     c,
 901                                   int*        ldc,
 902                                   double*     work,
 903                                   int*        lwork,
 904                                   int*        info);
 905
 906     void F77_FUNC(dorg2r,
 907                   DORG2R)(int* m, int* n, int* k, double* a, int* lda, double* tau, double* work, int* info);
 908
 909     void F77_FUNC(dlasq4, DLASQ4)(int*    i0,
 910                                   int*    n0,
 911                                   double* z,
 912                                   int*    pp,
 913                                   int*    n0in,
 914                                   double* dmin,
 915                                   double* dmin1,
 916                                   double* dmin2,
 917                                   double* dn,
 918                                   double* dn1,
 919                                   double* dn2,
 920                                   double* tau,
 921                                   int*    ttype);
 922
 923     void F77_FUNC(dlasd7, DLASD7)(int*    icompq,
 924                                   int*    nl,
 925                                   int*    nr,
 926                                   int*    sqre,
 927                                   int*    k,
 928                                   double* d,
 929                                   double* z,
 930                                   double* zw,
 931                                   double* vf,
 932                                   double* vfw,
 933                                   double* vl,
 934                                   double* vlw,
 935                                   double* alpha,
 936                                   double* beta,
 937                                   double* dsigma,
 938                                   int*    idx,
 939                                   int*    idxp,
 940                                   int*    idxq,
 941                                   int*    perm,
 942                                   int*    givptr,
 943                                   int*    givcol,
 944                                   int*    ldgcol,
 945                                   double* givnum,
 946                                   int*    ldgnum,
 947                                   double* c,
 948                                   double* s,
 949                                   int*    info);
 950
 951     void F77_FUNC(dlas2, DLAS2)(double* f, double* g, double* h, double* ssmin, double* ssmax);
 952
 953     void F77_FUNC(dlarfg, DLARFG)(int* n, double* alpha, double* x, int* incx, double* tau);
 954
 955     void F77_FUNC(dlagtf, DLAGTF)(int*    n,
 956                                   double* a,
 957                                   double* lambda,
 958                                   double* b,
 959                                   double* c,
 960                                   double* tol,
 961                                   double* d,
 962                                   int*    in,
 963                                   int*    info);
 964
 965     void F77_FUNC(dgeqrf,
 966                   DGEQRF)(int* m, int* n, double* a, int* lda, double* tau, double* work, int* lwork, int* info);
 967
 968
 969     /* Single precision */
 970
 971     void F77_FUNC(sbdsdc, SBDSDC)(const char* uplo,
 972                                   const char* compq,
 973                                   int*        n,
 974                                   float*      d,
 975                                   float*      e,
 976                                   float*      u,
 977                                   int*        ldu,
 978                                   float*      vt,
 979                                   int*        ldvt,
 980                                   float*      q,
 981                                   int*        iq,
 982                                   float*      work,
 983                                   int*        iwork,
 984                                   int*        info);
 985
 986     void F77_FUNC(sgetf2, SGETF2)(int* m, int* n, float* a, int* lda, int* ipiv, int* info);
 987
 988     void F77_FUNC(slamrg, SLAMRG)(int* n1, int* n2, float* a, int* dtrd1, int* dtrd2, int* index);
 989
 990     void F77_FUNC(slarnv, SLARNV)(int* idist, int* iseed, int* n, float* x);
 991
 992     void F77_FUNC(slasd0, SLASD0)(int*   n,
 993                                   int*   sqre,
 994                                   float* d,
 995                                   float* e,
 996                                   float* u,
 997                                   int*   ldu,
 998                                   float* vt,
 999                                   int*   ldvt,
1000                                   int*   smlsiz,
1001                                   int*   iwork,
1002                                   float* work,
1003                                   int*   info);
1004
1005     void F77_FUNC(slasda, SLASDA)(int*   icompq,
1006                                   int*   smlsiz,
1007                                   int*   n,
1008                                   int*   sqre,
1009                                   float* d,
1010                                   float* e,
1011                                   float* u,
1012                                   int*   ldu,
1013                                   float* vt,
1014                                   int*   k,
1015                                   float* difl,
1016                                   float* difr,
1017                                   float* z,
1018                                   float* poles,
1019                                   int*   givptr,
1020                                   int*   givcol,
1021                                   int*   ldgcol,
1022                                   int*   perm,
1023                                   float* givnum,
1024                                   float* c,
1025                                   float* s,
1026                                   float* work,
1027                                   int*   iwork,
1028                                   int*   info);
1029
1030     void F77_FUNC(slasq6, SLASQ6)(int*   i0,
1031                                   int*   n0,
1032                                   float* z,
1033                                   int*   pp,
1034                                   float* dmin,
1035                                   float* dmin1,
1036                                   float* dmin2,
1037                                   float* dn,
1038                                   float* dnm1,
1039                                   float* dnm2);
1040
1041     void F77_FUNC(sorgl2,
1042                   SORGL2)(int* m, int* n, int* k, float* a, int* lda, float* tau, float* work, int* info);
1043
1044     void F77_FUNC(sbdsqr, SBDSQR)(const char* uplo,
1045                                   int*        n,
1046                                   int*        ncvt,
1047                                   int*        nru,
1048                                   int*        ncc,
1049                                   float*      d,
1050                                   float*      e,
1051                                   float*      vt,
1052                                   int*        ldvt,
1053                                   float*      u,
1054                                   int*        ldu,
1055                                   float*      c,
1056                                   int*        ldc,
1057                                   float*      work,
1058                                   int*        info);
1059
1060     void F77_FUNC(sgetrf, SGETRF)(int* m, int* n, float* a, int* lda, int* ipiv, int* info);
1061
1062     void F77_FUNC(sgetri, SGETRI)(int* n, float* a, int* lda, int* ipiv, float* work, int* lwork, int* info);
1063
1064     void F77_FUNC(sgetrs, SGETRS)(const char* trans,
1065                                   int*        n,
1066                                   int*        nrhs,
1067                                   float*      a,
1068                                   int*        lda,
1069                                   int*        ipiv,
1070                                   float*      b,
1071                                   int*        ldb,
1072                                   int*        info);
1073
1074     void F77_FUNC(strtri, STRTRI)(const char* uplo, const char* diag, int* n, float* a, int* lda, int* info);
1075
1076     void F77_FUNC(strti2, STRTI2)(const char* uplo, const char* diag, int* n, float* a, int* lda, int* info);
1077
1078     float F77_FUNC(slange, SLANGE)(const char* norm, int* m, int* n, float* a, int* lda, float* work);
1079
1080     void F77_FUNC(slarrbx, SLARRBX)(int*   n,
1081                                     float* d,
1082                                     float* l,
1083                                     float* ld,
1084                                     float* lld,
1085                                     int*   ifirst,
1086                                     int*   ilast,
1087                                     float* rtol1,
1088                                     float* rtol2,
1089                                     int*   offset,
1090                                     float* w,
1091                                     float* wgap,
1092                                     float* werr,
1093                                     float* work,
1094                                     int*   iwork,
1095                                     int*   info);
1096
1097     void F77_FUNC(slasd1, SLASD1)(int*   nl,
1098                                   int*   nr,
1099                                   int*   sqre,
1100                                   float* d,
1101                                   float* alpha,
1102                                   float* beta,
1103                                   float* u,
1104                                   int*   ldu,
1105                                   float* vt,
1106                                   int*   ldvt,
1107                                   int*   idxq,
1108                                   int*   iwork,
1109                                   float* work,
1110                                   int*   info);
1111
1112     void F77_FUNC(slasdq, SLASDQ)(const char* uplo,
1113                                   int*        sqre,
1114                                   int*        n,
1115                                   int*        ncvt,
1116                                   int*        nru,
1117                                   int*        ncc,
1118                                   float*      d,
1119                                   float*      e,
1120                                   float*      vt,
1121                                   int*        ldvt,
1122                                   float*      u,
1123                                   int*        ldu,
1124                                   float*      c,
1125                                   int*        ldc,
1126                                   float*      work,
1127                                   int*        info);
1128
1129     void F77_FUNC(slasr, SLASR)(const char* side,
1130                                 const char* pivot,
1131                                 const char* direct,
1132                                 int*        m,
1133                                 int*        n,
1134                                 float*      c,
1135                                 float*      s,
1136                                 float*      a,
1137                                 int*        lda);
1138
1139     void F77_FUNC(sorglq,
1140                   SORGLQ)(int* m, int* n, int* k, float* a, int* lda, float* tau, float* work, int* lwork, int* info);
1141
1142     void F77_FUNC(sormtr, SORMTR)(const char* side,
1143                                   const char* uplo,
1144                                   const char* trans,
1145                                   int*        m,
1146                                   int*        n,
1147                                   float*      a,
1148                                   int*        lda,
1149                                   float*      tau,
1150                                   float*      c,
1151                                   int*        ldc,
1152                                   float*      work,
1153                                   int*        lwork,
1154                                   int*        info);
1155
1156     void F77_FUNC(sgebd2, SGEBD2)(int*   m,
1157                                   int*   n,
1158                                   float* a,
1159                                   int*   lda,
1160                                   float* d,
1161                                   float* e,
1162                                   float* tauq,
1163                                   float* taup,
1164                                   float* work,
1165                                   int*   info);
1166
1167     void F77_FUNC(slabrd, SLABRD)(int*   m,
1168                                   int*   n,
1169                                   int*   nb,
1170                                   float* a,
1171                                   int*   lda,
1172                                   float* d,
1173                                   float* e,
1174                                   float* tauq,
1175                                   float* taup,
1176                                   float* x,
1177                                   int*   ldx,
1178                                   float* y,
1179                                   int*   ldy);
1180
1181     float F77_FUNC(slanst, SLANST)(const char* norm, int* n, float* d, float* e);
1182
1183     float F77_FUNC(slansy,
1184                    SLANSY)(const char* norm, const char* uplo, int* n, float* a, int* lda, float* work);
1185
1186     void F77_FUNC(slarrex, SLARREX)(const char* range,
1187                                     int*        n,
1188                                     float*      vl,
1189                                     float*      vu,
1190                                     int*        il,
1191                                     int*        iu,
1192                                     float*      d,
1193                                     float*      e,
1194                                     float*      tol,
1195                                     int*        nsplit,
1196                                     int*        isplit,
1197                                     int*        m,
1198                                     float*      w,
1199                                     int*        iblock,
1200                                     int*        indexw,
1201                                     float*      gersch,
1202                                     float*      work,
1203                                     int*        iwork,
1204                                     int*        info);
1205
1206     void F77_FUNC(slasd2, SLASD2)(int*   nl,
1207                                   int*   nr,
1208                                   int*   sqre,
1209                                   int*   k,
1210                                   float* d,
1211                                   float* z,
1212                                   float* alpha,
1213                                   float* beta,
1214                                   float* u,
1215                                   int*   ldu,
1216                                   float* vt,
1217                                   int*   ldvt,
1218                                   float* dsigma,
1219                                   float* u2,
1220                                   int*   ldu2,
1221                                   float* vt2,
1222                                   int*   ldvt2,
1223                                   int*   idxp,
1224                                   int*   idx,
1225                                   int*   idxc,
1226                                   int*   idxq,
1227                                   int*   coltyp,
1228                                   int*   info);
1229
1230     void F77_FUNC(slasdt, SLASDT)(int* n, int* lvl, int* nd, int* inode, int* ndiml, int* ndimr, int* msub);
1231
1232     void F77_FUNC(slasrt, SLASRT)(const char* id, int* n, float* d, int* info);
1233
1234     void F77_FUNC(slasrt2, SLASRT2)(const char* id, int* n, float* d, int* key, int* info);
1235
1236     void F77_FUNC(sorgqr,
1237                   SORGQR)(int* m, int* n, int* k, float* a, int* lda, float* tau, float* work, int* lwork, int* info);
1238
1239     void F77_FUNC(sstebz, SSTEBZ)(const char* range,
1240                                   const char* order,
1241                                   int*        n,
1242                                   float*      vl,
1243                                   float*      vu,
1244                                   int*        il,
1245                                   int*        iu,
1246                                   float*      abstol,
1247                                   float*      d,
1248                                   float*      e,
1249                                   int*        m,
1250                                   int*        nsplit,
1251                                   float*      w,
1252                                   int*        iblock,
1253                                   int*        isplit,
1254                                   float*      work,
1255                                   int*        iwork,
1256                                   int*        info);
1257
1258     void F77_FUNC(sgebrd, SGEBRD)(int*   m,
1259                                   int*   n,
1260                                   float* a,
1261                                   int*   lda,
1262                                   float* d,
1263                                   float* e,
1264                                   float* tauq,
1265                                   float* taup,
1266                                   float* work,
1267                                   int*   lwork,
1268                                   int*   info);
1269
1270     void F77_FUNC(slacpy, SLACPY)(const char* uplo, int* m, int* n, float* a, int* lda, float* b, int* ldb);
1271
1272     float F77_FUNC(slapy2, SLAPY2)(float* x, float* y);
1273
1274     void F77_FUNC(slarrfx, SLARRFX)(int*   n,
1275                                     float* d,
1276                                     float* l,
1277                                     float* ld,
1278                                     float* lld,
1279                                     int*   ifirst,
1280                                     int*   ilast,
1281                                     float* w,
1282                                     float* sigma,
1283                                     float* dplus,
1284                                     float* lplus,
1285                                     float* work,
1286                                     int*   info);
1287
1288     void F77_FUNC(slasd3, SLASD3)(int*   nl,
1289                                   int*   nr,
1290                                   int*   sqre,
1291                                   int*   k,
1292                                   float* d,
1293                                   float* q,
1294                                   int*   ldq,
1295                                   float* dsigma,
1296                                   float* u,
1297                                   int*   ldu,
1298                                   float* u2,
1299                                   int*   ldu2,
1300                                   float* vt,
1301                                   int*   ldvt,
1302                                   float* vt2,
1303                                   int*   ldvt2,
1304                                   int*   idxc,
1305                                   int*   ctot,
1306                                   float* z,
1307                                   int*   info);
1308
1309     void F77_FUNC(slaset,
1310                   SLASET)(const char* uplo, int* m, int* n, float* alpha, float* beta, float* a, int* lda);
1311
1312     void F77_FUNC(slassq, SLASSQ)(int* n, float* x, int* incx, float* scale, float* sumsq);
1313
1314     void F77_FUNC(sorm2l, SORM2L)(const char* side,
1315                                   const char* trans,
1316                                   int*        m,
1317                                   int*        n,
1318                                   int*        k,
1319                                   float*      a,
1320                                   int*        lda,
1321                                   float*      tau,
1322                                   float*      c,
1323                                   int*        ldc,
1324                                   float*      work,
1325                                   int*        info);
1326
1327     void F77_FUNC(sstegr, SSTEGR)(const char* jobz,
1328                                   const char* range,
1329                                   int*        n,
1330                                   float*      d,
1331                                   float*      e,
1332                                   float*      vl,
1333                                   float*      vu,
1334                                   int*        il,
1335                                   int*        iu,
1336                                   float*      abstol,
1337                                   int*        m,
1338                                   float*      w,
1339                                   float*      z,
1340                                   int*        ldz,
1341                                   int*        isuppz,
1342                                   float*      work,
1343                                   int*        lwork,
1344                                   int*        iwork,
1345                                   int*        liwork,
1346                                   int*        info);
1347
1348     void F77_FUNC(sgelq2, SGELQ2)(int* m, int* n, float* a, int* lda, float* tau, float* work, int* info);
1349
1350     void F77_FUNC(slae2, SLAE2)(float* a, float* b, float* c, float* rt1, float* rt2);
1351
1352     void F77_FUNC(slaev2,
1353                   SLAEV2)(float* a, float* b, float* c, float* rt1, float* rt2, float* cs1, float* cs2);
1354
1355     void F77_FUNC(slar1vx, SLAR1VX)(int*   n,
1356                                     int*   b1,
1357                                     int*   bn,
1358                                     float* sigma,
1359                                     float* d,
1360                                     float* l,
1361                                     float* ld,
1362                                     float* lld,
1363                                     float* eval,
1364                                     float* gersch,
1365                                     float* z,
1366                                     float* ztz,
1367                                     float* mingma,
1368                                     int*   r,
1369                                     int*   isuppz,
1370                                     float* work);
1371
1372     void F77_FUNC(slarrvx, SLARRVX)(int*   n,
1373                                     float* d,
1374                                     float* l,
1375                                     int*   isplit,
1376                                     int*   m,
1377                                     float* w,
1378                                     int*   iblock,
1379                                     int*   indexw,
1380                                     float* gersch,
1381                                     float* tol,
1382                                     float* z,
1383                                     int*   ldz,
1384                                     int*   isuppz,
1385                                     float* work,
1386                                     int*   iwork,
1387                                     int*   info);
1388
1389     void F77_FUNC(slasd4, SLASD4)(int*   n,
1390                                   int*   i,
1391                                   float* d,
1392                                   float* z,
1393                                   float* delta,
1394                                   float* rho,
1395                                   float* sigma,
1396                                   float* work,
1397                                   int*   info);
1398
1399     void F77_FUNC(slasq1, SLASQ1)(int* n, float* d, float* e, float* work, int* info);
1400
1401
1402     void F77_FUNC(slasv2, SLASV2)(float* f,
1403                                   float* g,
1404                                   float* h,
1405                                   float* ssmin,
1406                                   float* ssmax,
1407                                   float* snr,
1408                                   float* csr,
1409                                   float* snl,
1410                                   float* csl);
1411
1412     void F77_FUNC(sorm2r, SORM2R)(const char* side,
1413                                   const char* trans,
1414                                   int*        m,
1415                                   int*        n,
1416                                   int*        k,
1417                                   float*      a,
1418                                   int*        lda,
1419                                   float*      tau,
1420                                   float*      c,
1421                                   int*        ldc,
1422                                   float*      work,
1423                                   int*        info);
1424
1425     void F77_FUNC(sstein, SSTEIN)(int*   n,
1426                                   float* d,
1427                                   float* e,
1428                                   int*   m,
1429                                   float* w,
1430                                   int*   iblock,
1431                                   int*   isplit,
1432                                   float* z,
1433                                   int*   ldz,
1434                                   float* work,
1435                                   int*   iwork,
1436                                   int*   ifail,
1437                                   int*   info);
1438
1439     void F77_FUNC(sgelqf,
1440                   SGELQF)(int* m, int* n, float* a, int* lda, float* tau, float* work, int* lwork, int* info);
1441
1442     void F77_FUNC(slaebz, SLAEBZ)(int*   ijob,
1443                                   int*   nitmax,
1444                                   int*   n,
1445                                   int*   mmax,
1446                                   int*   minp,
1447                                   int*   nbmin,
1448                                   float* abstol,
1449                                   float* reltol,
1450                                   float* pivmin,
1451                                   float* d,
1452                                   float* e,
1453                                   float* e2,
1454                                   int*   nval,
1455                                   float* ab,
1456                                   float* c,
1457                                   int*   mout,
1458                                   int*   nab,
1459                                   float* work,
1460                                   int*   iwork,
1461                                   int*   info);
1462
1463     void F77_FUNC(slarf,
1464                   SLARF)(const char* side, int* m, int* n, float* v, int* incv, float* tau, float* c, int* ldc, float* work);
1465
1466     void F77_FUNC(slartg, SLARTG)(float* f, float* g, float* cs, float* sn, float* r);
1467
1468     void F77_FUNC(slasd5,
1469                   SLASD5)(int* i, float* d, float* z, float* delta, float* rho, float* dsigma, float* work);
1470
1471     void F77_FUNC(slasq2, SLASQ2)(int* n, float* z, int* info);
1472
1473     void F77_FUNC(slasq3, SLASQ3)(int*   i0,
1474                                   int*   n0,
1475                                   float* z,
1476                                   int*   pp,
1477                                   float* dmin,
1478                                   float* sigma,
1479                                   float* desig,
1480                                   float* qmax,
1481                                   int*   nfail,
1482                                   int*   iter,
1483                                   int*   ndiv,
1484                                   int*   ieee);
1485
1486     void F77_FUNC(slaswp, SLASWP)(int* n, float* a, int* lda, int* k1, int* k2, int* ipiv, int* incx);
1487
1488     void F77_FUNC(sormbr, SORMBR)(const char* vect,
1489                                   const char* side,
1490                                   const char* trans,
1491                                   int*        m,
1492                                   int*        n,
1493                                   int*        k,
1494                                   float*      a,
1495                                   int*        lda,
1496                                   float*      tau,
1497                                   float*      c,
1498                                   int*        ldc,
1499                                   float*      work,
1500                                   int*        lwork,
1501                                   int*        info);
1502
1503     void F77_FUNC(ssterf, SSTERF)(int* n, float* d, float* e, int* info);
1504
1505     void F77_FUNC(sgeqr2, SGEQR2)(int* m, int* n, float* a, int* lda, float* tau, float* work, int* info);
1506
1507     void F77_FUNC(slaed6,
1508                   SLAED6)(int* kniter, int* orgati, float* rho, float* d, float* z, float* finit, float* tau, int* info);
1509
1510     void F77_FUNC(slarfb, SLARFB)(const char* side,
1511                                   const char* trans,
1512                                   const char* direct,
1513                                   const char* storev,
1514                                   int*        m,
1515                                   int*        n,
1516                                   int*        k,
1517                                   float*      v,
1518                                   int*        ldv,
1519                                   float*      t,
1520                                   int*        ldt,
1521                                   float*      c,
1522                                   int*        ldc,
1523                                   float*      work,
1524                                   int*        ldwork);
1525
1526     void F77_FUNC(slaruv, SLARUV)(int* iseed, int* n, float* x);
1527
1528     void F77_FUNC(slasd6, SLASD6)(int*   icompq,
1529                                   int*   nl,
1530                                   int*   nr,
1531                                   int*   sqre,
1532                                   float* d,
1533                                   float* vf,
1534                                   float* vl,
1535                                   float* alpha,
1536                                   float* beta,
1537                                   int*   idxq,
1538                                   int*   perm,
1539                                   int*   givptr,
1540                                   int*   givcol,
1541                                   int*   ldgcol,
1542                                   float* givnum,
1543                                   int*   ldgnum,
1544                                   float* poles,
1545                                   float* difl,
1546                                   float* difr,
1547                                   float* z,
1548                                   int*   k,
1549                                   float* c,
1550                                   float* s,
1551                                   float* work,
1552                                   int*   iwork,
1553                                   int*   info);
1554
1555     void F77_FUNC(slatrd,
1556                   SLATRD)(const char* uplo, int* n, int* nb, float* a, int* lda, float* e, float* tau, float* w, int* ldw);
1557
1558     void F77_FUNC(sorml2, SORML2)(const char* side,
1559                                   const char* trans,
1560                                   int*        m,
1561                                   int*        n,
1562                                   int*        k,
1563                                   float*      a,
1564                                   int*        lda,
1565                                   float*      tau,
1566                                   float*      c,
1567                                   int*        ldc,
1568                                   float*      work,
1569                                   int*        info);
1570
1571     void F77_FUNC(sstevr, SSTEVR)(const char* jobz,
1572                                   const char* range,
1573                                   int*        n,
1574                                   float*      d,
1575                                   float*      e,
1576                                   float*      vl,
1577                                   float*      vu,
1578                                   int*        il,
1579                                   int*        iu,
1580                                   float*      abstol,
1581                                   int*        m,
1582                                   float*      w,
1583                                   float*      z,
1584                                   int*        ldz,
1585                                   int*        isuppz,
1586                                   float*      work,
1587                                   int*        lwork,
1588                                   int*        iwork,
1589                                   int*        liwork,
1590                                   int*        info);
1591
1592     void F77_FUNC(ssytrd, SSYTRD)(const char* uplo,
1593                                   int*        n,
1594                                   float*      a,
1595                                   int*        lda,
1596                                   float*      d,
1597                                   float*      e,
1598                                   float*      tau,
1599                                   float*      work,
1600                                   int*        lwork,
1601                                   int*        info);
1602
1603     void F77_FUNC(ssyevr, SSYEVR)(const char* jobz,
1604                                   const char* range,
1605                                   const char* uplo,
1606                                   int*        n,
1607                                   float*      a,
1608                                   int*        lda,
1609                                   float*      vl,
1610                                   float*      vu,
1611                                   int*        il,
1612                                   int*        iu,
1613                                   float*      abstol,
1614                                   int*        m,
1615                                   float*      w,
1616                                   float*      z__,
1617                                   int*        ldz,
1618                                   int*        isuppz,
1619                                   float*      work,
1620                                   int*        lwork,
1621                                   int*        iwork,
1622                                   int*        liwork,
1623                                   int*        info);
1624
1625     void F77_FUNC(sormql, SORMQL)(const char* side,
1626                                   const char* trans,
1627                                   int*        m,
1628                                   int*        n,
1629                                   int*        k,
1630                                   float*      a,
1631                                   int*        lda,
1632                                   float*      tau,
1633                                   float*      c,
1634                                   int*        ldc,
1635                                   float*      work,
1636                                   int*        lwork,
1637                                   int*        info);
1638
1639     void F77_FUNC(sormqr, SORMQR)(const char* side,
1640                                   const char* trans,
1641                                   int*        m,
1642                                   int*        n,
1643                                   int*        k,
1644                                   float*      a,
1645                                   int*        lda,
1646                                   float*      tau,
1647                                   float*      c,
1648                                   int*        ldc,
1649                                   float*      work,
1650                                   int*        lwork,
1651                                   int*        info);
1652
1653     void F77_FUNC(sorgbr, SORGBR)(const char* vect,
1654                                   int*        m,
1655                                   int*        n,
1656                                   int*        k,
1657                                   float*      a,
1658                                   int*        lda,
1659                                   float*      tau,
1660                                   float*      work,
1661                                   int*        lwork,
1662                                   int*        info);
1663
1664     void F77_FUNC(slasq5, SLASQ5)(int*   i0,
1665                                   int*   n0,
1666                                   float* z,
1667                                   int*   pp,
1668                                   float* tau,
1669                                   float* dmin,
1670                                   float* dmin1,
1671                                   float* dmin2,
1672                                   float* dn,
1673                                   float* dnm1,
1674                                   float* dnm2,
1675                                   int*   ieee);
1676
1677     void F77_FUNC(slasd8, SLASD8)(int*   icompq,
1678                                   int*   k,
1679                                   float* d,
1680                                   float* z,
1681                                   float* vf,
1682                                   float* vl,
1683                                   float* difl,
1684                                   float* difr,
1685                                   int*   lddifr,
1686                                   float* dsigma,
1687                                   float* work,
1688                                   int*   info);
1689
1690     void F77_FUNC(slascl, SLASCL)(const char* type,
1691                                   int*        kl,
1692                                   int*        ku,
1693                                   float*      cfrom,
1694                                   float*      cto,
1695                                   int*        m,
1696                                   int*        n,
1697                                   float*      a,
1698                                   int*        lda,
1699                                   int*        info);
1700
1701     void F77_FUNC(slarft, SLARFT)(const char* direct,
1702                                   const char* storev,
1703                                   int*        n,
1704                                   int*        k,
1705                                   float*      v,
1706                                   int*        ldv,
1707                                   float*      tau,
1708                                   float*      t,
1709                                   int*        ldt);
1710
1711     void F77_FUNC(slagts,
1712                   SLAGTS)(int* job, int* n, float* a, float* b, float* c, float* d, int* in, float* y, float* tol, int* info);
1713
1714     void F77_FUNC(sgesdd, SGESDD)(const char* jobz,
1715                                   int*        m,
1716                                   int*        n,
1717                                   float*      a,
1718                                   int*        lda,
1719                                   float*      s,
1720                                   float*      u,
1721                                   int*        ldu,
1722                                   float*      vt,
1723                                   int*        ldvt,
1724                                   float*      work,
1725                                   int*        lwork,
1726                                   int*        iwork,
1727                                   int*        info);
1728
1729     void F77_FUNC(ssytd2,
1730                   SSYTD2)(const char* uplo, int* n, float* a, int* lda, float* d, float* e, float* tau, int* info);
1731
1732     void F77_FUNC(sormlq, SORMLQ)(const char* side,
1733                                   const char* trans,
1734                                   int*        m,
1735                                   int*        n,
1736                                   int*        k,
1737                                   float*      a,
1738                                   int*        lda,
1739                                   float*      tau,
1740                                   float*      c,
1741                                   int*        ldc,
1742                                   float*      work,
1743                                   int*        lwork,
1744                                   int*        info);
1745
1746     void F77_FUNC(sorg2r,
1747                   SORG2R)(int* m, int* n, int* k, float* a, int* lda, float* tau, float* work, int* info);
1748
1749     void F77_FUNC(slasq4, SLASQ4)(int*   i0,
1750                                   int*   n0,
1751                                   float* z,
1752                                   int*   pp,
1753                                   int*   n0in,
1754                                   float* dmin,
1755                                   float* dmin1,
1756                                   float* dmin2,
1757                                   float* dn,
1758                                   float* dn1,
1759                                   float* dn2,
1760                                   float* tau,
1761                                   int*   ttype);
1762
1763     void F77_FUNC(slasd7, SLASD7)(int*   icompq,
1764                                   int*   nl,
1765                                   int*   nr,
1766                                   int*   sqre,
1767                                   int*   k,
1768                                   float* d,
1769                                   float* z,
1770                                   float* zw,
1771                                   float* vf,
1772                                   float* vfw,
1773                                   float* vl,
1774                                   float* vlw,
1775                                   float* alpha,
1776                                   float* beta,
1777                                   float* dsigma,
1778                                   int*   idx,
1779                                   int*   idxp,
1780                                   int*   idxq,
1781                                   int*   perm,
1782                                   int*   givptr,
1783                                   int*   givcol,
1784                                   int*   ldgcol,
1785                                   float* givnum,
1786                                   int*   ldgnum,
1787                                   float* c,
1788                                   float* s,
1789                                   int*   info);
1790
1791     void F77_FUNC(slas2, SLAS2)(float* f, float* g, float* h, float* ssmin, float* ssmax);
1792
1793     void F77_FUNC(slarfg, SLARFG)(int* n, float* alpha, float* x, int* incx, float* tau);
1794
1795     void F77_FUNC(slagtf,
1796                   SLAGTF)(int* n, float* a, float* lambda, float* b, float* c, float* tol, float* d, int* in, int* info);
1797
1798     void F77_FUNC(sgeqrf,
1799                   SGEQRF)(int* m, int* n, float* a, int* lda, float* tau, float* work, int* lwork, int* info);
1800
1801
1802 #ifdef __cplusplus
1803 }
1804 #endif
1805
1806 /*! \endcond */
1807
1808 #endif /* GMX_LAPACK_H */